Preheat oven to 400F.
Lay the two sheets of thawed puff pastry out flat on a clean work surface.
Use a sharp knife to cut each sheet into 6 rectangles, making 12 total rectangles.
Use the knife to score a ½ inch border around each rectangle (only cut about ½ way down into the dough). This will allow the outside ½ inch border to puff up while baking and the middle to stay flatter.
Use a fork to prick several areas around the middle of each rectangle of pastry.
This helps to keep the center from rising too much while baking.
Place the pastries onto one large or two medium baking sheets, about 1 inch apart.
In a medium mixing bowl, use an electric mixer to beat together the cream cheese, granulated sugar, and 1 teaspoon of the vanilla extract.
Scoop the mixture onto the pastries and spread out evenly over the center area, but not onto the ½ inch border.
In a small bowl, whisk together the egg and water.
Use a pastry brush to lightly brush the egg wash onto the ½ inch border of each pastry.
Bake the pastries at 400F for 18-20 minutes until the pastry is puffed up and golden brown.
Remove from the oven and transfer the pastries to a wire cooling rack.
While the pastries are still warm, add a spoonful of the cherry pie filling to the center of each pastry and spread out just enough to mostly cover the cream cheese layer.
In a small bowl, whisk together the powdered sugar, heavy cream, and remaining ½ teaspoon vanilla extract.
Drizzle the frosting over the cooled pastries.